18 research outputs found
The Lyth Bound and the End of Inflation
We derive an extended version of the well-known Lyth Bound on the total
variation of the inflaton field, incorporating higher order corrections in slow
roll. We connect the field variation to both the spectral index of
scalar perturbations and the amplitude of tensor modes. We then investigate the
implications of this bound for ``small field'' potentials, where the field
rolls off a local maximum of the potential. The total field variation during
inflation is {\em generically} of order , even for potentials with
a suppressed tensor/scalar ratio. Much of the total field excursion arises in
the last e-fold of inflation and in single field models this problem can only
be avoided via fine-tuning or the imposition of a symmetry. Finally, we discuss
the implications of this result for inflationary model building in string
theory and supergravity.Comment: 10 pages, RevTeX, 2 figures (V3: version accepted for publication by
JCAP
Cosmology From Random Multifield Potentials
We consider the statistical properties of vacua and inflationary trajectories
associated with a random multifield potential. Our underlying motivation is the
string landscape, but our calculations apply to general potentials. Using
random matrix theory, we analyze the Hessian matrices associated with the
extrema of this potential. These potentials generically have a vast number of
extrema. If the cross-couplings (off-diagonal terms) are of the same order as
the self-couplings (diagonal terms) we show that essentially all extrema are
saddles, and the number of minima is effectively zero. Avoiding this requires
the same separation of scales needed to ensure that Newton's constant is stable
against radiative corrections in a string landscape. Using the central limit
theorem we find that even if the number of extrema is enormous, the typical
distance between extrema is still substantial -- with challenging implications
for inflationary models that depend on the existence of a complicated path
inside the landscape.Comment: revtex, 3 figures, 10 pages v2 refs adde
Multi-field Inflation with a Random Potential
Motivated by the possibility of inflation in the cosmic landscape, which may
be approximated by a complicated potential, we study the density perturbations
in multi-field inflation with a random potential. The random potential causes
the inflaton to undergo a Brownian motion with a drift in the D-dimensional
field space. To quantify such an effect, we employ a stochastic approach to
evaluate the two-point and three-point functions of primordial perturbations.
We find that in the weakly random scenario the resulting power spectrum
resembles that of the single field slow-roll case, with up to 2% more red tilt.
The strongly random scenario, leads to rich phenomenologies, such as primordial
fluctuations in the power spectrum on all angular scales. Such features may
already be hiding in the error bars of observed CMB TT (as well as TE and EE)
power spectrum and can be detected or falsified with more data coming in the
future. The tensor power spectrum itself is free of fluctuations and the tensor
to scalar ratio is enhanced. In addition a large negative running of the power
spectral index is possible. Non-Gaussianity is generically suppressed by the
growth of adiabatic perturbations on super-horizon scales, but can possibly be
enhanced by resonant effects or arise from the entropic perturbations during
the onset of (p)reheating. The formalism developed in this paper can be applied
to a wide class of multi-field inflation models including, e.g. the N-flation
scenario.Comment: More clarifications and references adde
Multi-field Inflation with a Random Potential
Motivated by the possibility of inflation in the cosmic landscape, which may
be approximated by a complicated potential, we study the density perturbations
in multi-field inflation with a random potential. The random potential causes
the inflaton to undergo a Brownian motion with a drift in the D-dimensional
field space. To quantify such an effect, we employ a stochastic approach to
evaluate the two-point and three-point functions of primordial perturbations.
We find that in the weakly random scenario the resulting power spectrum
resembles that of the single field slow-roll case, with up to 2% more red tilt.
The strongly random scenario, leads to rich phenomenologies, such as primordial
fluctuations in the power spectrum on all angular scales. Such features may
already be hiding in the error bars of observed CMB TT (as well as TE and EE)
power spectrum and can be detected or falsified with more data coming in the
future. The tensor power spectrum itself is free of fluctuations and the tensor
to scalar ratio is enhanced. In addition a large negative running of the power
spectral index is possible. Non-Gaussianity is generically suppressed by the
growth of adiabatic perturbations on super-horizon scales, but can possibly be
enhanced by resonant effects or arise from the entropic perturbations during
the onset of (p)reheating. The formalism developed in this paper can be applied
to a wide class of multi-field inflation models including, e.g. the N-flation
scenario.Comment: More clarifications and references adde
Accidental Inflation in the Landscape
We study some aspects of fine tuning in inflationary scenarios within string
theory flux compactifications and, in particular, in models of accidental
inflation. We investigate the possibility that the apparent fine-tuning of the
low energy parameters of the theory needed to have inflation can be generically
obtained by scanning the values of the fluxes over the landscape. Furthermore,
we find that the existence of a landscape of eternal inflation in this model
provides us with a natural theory of initial conditions for the inflationary
period in our vacuum. We demonstrate how these two effects work in a small
corner of the landscape associated with the complex structure of the Calabi-Yau
manifold P^4_[1,1,1,6,9] by numerically investigating the flux vacua of a
reduced moduli space. This allows us to obtain the distribution of observable
parameters for inflation in this mini-landscape directly from the fluxes.Comment: 40 pages, 11 figure
A Global View on The Search for de-Sitter Vacua in (type IIA) String Theory
The search for classically stable Type IIA de-Sitter vacua typically starts
with an ansatz that gives Anti-de-Sitter supersymmetric vacua and then raises
the cosmological constant by modifying the compactification. As one raises the
cosmological constant, the couplings typically destabilize the classically
stable vacuum, so the probability that this approach will lead to a classically
stable de-Sitter vacuum is Gaussianly suppressed. This suggests that
classically stable de-Sitter vacua in string theory (at least in the Type IIA
region), especially those with relatively high cosmological constants, are very
rare. The probability that a typical de-Sitter extremum is classically stable
(i.e., tachyon-free) is argued to be Gaussianly suppressed as a function of the
number of moduli.Comment: 23 pages, 5 figures; v2, v3: arguments improved, references added;
v4: version to appear in JHE